Problem: Solve for $x$ and $y$ using elimination. ${3x+2y = 17}$ ${2x-2y = -2}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $5x = 15$ $\dfrac{5x}{{5}} = \dfrac{15}{{5}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {3x+2y = 17}\thinspace$ to find $y$ ${3}{(3)}{ + 2y = 17}$ $9+2y = 17$ $9{-9} + 2y = 17{-9}$ $2y = 8$ $\dfrac{2y}{{2}} = \dfrac{8}{{2}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {2x-2y = -2}\thinspace$ and get the same answer for $y$ : ${2}{(3)}{ - 2y = -2}$ ${y = 4}$